Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Mar 2011
Posts: 78

If i and d are integers, what is the value of i? [#permalink]
Show Tags
26 May 2011, 20:25
9
This post was BOOKMARKED
Question Stats:
59% (03:02) correct
41% (01:52) wrong based on 236 sessions
HideShow timer Statistics
If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d (2) The quotient when i is divided by (d+2) is d What is the best way to tackle this kind of DS problems?
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 07 Feb 2012, 07:32, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 39755

Re: What is the best way to tackle this kind of DS problems [#permalink]
Show Tags
07 Feb 2012, 07:31
smodak wrote: If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d (2) The quotient when i is divided by (d+2) is d
What is the best way to tackle this kind of DS problems?
It can be done algebraically but picking numbers would probably be faster/easier. If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d > let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 > if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient. (2) The quotient when i is divided by (d+2) is d > let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient. (1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5. Answer: E. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: What is the best way to tackle this kind of DS problems [#permalink]
Show Tags
13 May 2014, 16:12
Bunuel wrote: smodak wrote: If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d (2) The quotient when i is divided by (d+2) is d
What is the best way to tackle this kind of DS problems?
It can be done algebraically but picking numbers would probably be faster/easier. If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d > let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 > if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient. (2) The quotient when i is divided by (d+2) is d > let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient. (1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5. Answer: E. Hope it's clear. What's the trick in this question? Is it only the fact that 'd' and 'd+2' as denominators can be larger than 'i' and therefore, 'i' could take any value as long as it is smaller than the denominator as well as being a multiple of both 'd' and 'd+2' ? (Has to be a multiple otherwise remainder can't be zero) What do you guys thimk? Cheers J



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: What is the best way to tackle this kind of DS problems [#permalink]
Show Tags
30 May 2014, 06:07
Bunuel wrote: smodak wrote: If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d (2) The quotient when i is divided by (d+2) is d
What is the best way to tackle this kind of DS problems?
It can be done algebraically but picking numbers would probably be faster/easier. If i and d are integers, what is the value of i? (1) The remainder when i is divided by (d+2) is the same as when i is divided by d > let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 > if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient. (2) The quotient when i is divided by (d+2) is d > let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient. (1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5. Answer: E. Hope it's clear. Can this somehow be done algebraically or conceptually I had that first i/ (d+2) and i/d, yield the same remainder, but if both d and d+2, are larger than i, then 'i' could just take any value as the remainder. Clearly insufficient Statement 2 we have that i = (d)(d+2) + r Now, if we replace in first term, we have that (d)(d+2) + r / (d+2), gives d as quotient but still we are left with r as a remainder of d+2. while we also know that i/d gives the same remainder. Here we learn that 'i' must be greater than d+2 since if gives quotient d. However, we still have no clue as to what remainder the division can yield Both together, i>d, i = d(d+2) + r, and 'r' here is equal to the remainder of i/d = d(d+2) / d. So r/d = r/d+2, but still no information on the remainder Hence answer is E



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7450
Location: Pune, India

Re: If i and d are integers, what is the value of i? [#permalink]
Show Tags
17 Jun 2014, 22:05
smodak wrote: If i and d are integers, what is the value of i?
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d (2) The quotient when i is divided by (d+2) is d
What is the best way to tackle this kind of DS problems? Question: What is the value of i? How do you express stmnt 1 in an equation? Stmnt 1: The remainder when i is divided by (d+2) is the same as when i is divided by d. Say when i is divided by d or d + 2, the remainder we obtain is r. Does this mean that if we subtract r from i, whatever is leftover will be divisible by d as well as (d+2)? So assuming that d and d+2 do not have any common factors (even if they do have common factors other than 1, they can only have 2 as a common factor), we can put it down as i  r = d(d + 2)k i = d(d + 2)k + r Now for different values of d, k and r, values of i will be different. Stmnt 2: The quotient when i is divided by (d+2) is d This tells us that i = d(d +2) + r Now for different values of d and r, values of i will be different. Using both, we know that k is 1. But for different values of d and r, we can still have different values of i. Not sufficient. Answer (E)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16027

Re: If i and d are integers, what is the value of i? [#permalink]
Show Tags
01 Jul 2015, 06:37
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16027

Re: If i and d are integers, what is the value of i? [#permalink]
Show Tags
29 Sep 2016, 00:32
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 27 Feb 2015
Posts: 59
Concentration: General Management, Economics
WE: Engineering (Transportation)

Re: If i and d are integers, what is the value of i? [#permalink]
Show Tags
29 Sep 2016, 02:50
1. d+2=iq+r & d=iq'+r ( q : quotient and r : remainder ) subtract 2 equations We get, 2=i(qq') we dont know q and q'  INSUFFICENT
2. q'=d clearly INSUFFICIENT
both together, substitute value of q' in 1. we get, 2=i(qd) We don't have values of q and d INSUFFICIENT
ans E




Re: If i and d are integers, what is the value of i?
[#permalink]
29 Sep 2016, 02:50








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


10


The product of integers a, b, c, and d is 120. What is the value of in

Bunuel 
11 
25 Apr 2017, 15:34 

6


What is the value of a twodigit positive integer n, where i

fozzzy 
6 
15 Mar 2016, 10:10 

12


If a, b, c, and d are positive integers, what is the value..

daviesj 
11 
29 Nov 2016, 05:22 

1


What is the value of x? (i) Distance of x from y is the same

gmatbull 
13 
21 Feb 2011, 01:01 

12


What is the value of the integer k?

msand 
12 
18 Jul 2016, 01:55 



